Parkinson's Disease — Bayesian Causal Analysis (Pearl SCM)

Pearl Structural Causal Model — Live

Active protective intervention

Active risk exposure

Endpoint

Inactive node

Causal pathway

Dose–Response Saturation (Hill Equation)

Effect(d) = Effect_max × d^n / (d^n + EC50^n) [Hill, n typically 1–3]

Pareto Frontier — Cumulative Risk Reduction

Interventions ranked by individual effect, then added cumulatively (left→right). The curve is the joint risk reduction (1 − Pearl-adjusted joint HR), rising with each addition and saturating as cross-correlated mechanisms overlap. Gold points are active in your current selection.

E-Value (VanderWeele) — Unmeasured Confounding Robustness

E-value = HR + √(HR × (HR − 1)) for HR>1 | invert HR if <1

Higher E-value = more robust to unmeasured confounding. An unmeasured confounder would need to associate with both intervention and PD by ≥E-value (on RR scale) to nullify the observed effect.

Cross-Correlation Matrix — Pearl Backdoor Adjustment

ln(HR_joint) = ∑ α_i · ln(HR_i)
α_i = eigenvector deflation factor from Σ = QΛQᵀ

Positive correlation → shared mediator (e.g., exercise ↔ Mediterranean diet share inflammation reduction).
Negative correlation → independent pathways. Eigendecomposition orthogonalises the joint effect.

Causal Estimates

Joint Pearl-Adjusted HR

1.00

Baseline reference (no interventions)

95% CI (cross-corr adj.) [0.90, 1.10]

Risk vs Protection Decomposition

Σ Protective ln(HR) 0.00

Σ Risk ln(HR) 0.00

Net ln(HR) (raw) 0.00

Cross-corr deflation 0%

Net ln(HR) (Pearl-adj) 0.00

Counterfactual Probabilities

Baseline P(PD by 80)3.0%

P(PD | do(stack)) 3.0%

Risk Difference (RD) 0.0%

Number Needed (NNT) ∞

PNS lower bound 0.00

PNS upper bound 0.00

Worst-Case Sensitivity

Min E-value (active) —

Robust to confounding —

Active interventions 0

Methodology

Pearl backdoor criterion verified for each path. Cross-correlations between interventions estimated from shared mechanism categories (mitochondrial, autophagy, inflammation, gut-brain, dopaminergic). Eigendecomposition Σ = QΛQᵀ deflates redundant pathways. Counterfactual bounds via Tian-Pearl. E-values via VanderWeele & Ding (2017).